Knowledge Bank

``Bond Strength'' is a term which is much used but seldom (if ever) defined. A possible definition would be that the bond strength is the average force S required to do 99.99 per cent of the work necessary to produce infinite separation of the atoms X and Y in the $X-Y$ bond. That is ""[FIGURE]"" \begin{equation}S= \int^{R}{r{v}} f(r)\ dr/ \int^{R}{r{e}}dr,\end{equation} where $f(r)$ is the force at the internuclear separation $rire$ is the separation at equilibrium, and R is that value of r at which the potential energy $UR=0.9999WDeWDe$ being the dissociation energy (or bond energy). Using the Morse potential energy function, with $UR=0.9999WDe$ and $r=R$, one finds that $R-re=9.900/a$, where a is the constant in the Morse function that determines the curvature of the potential energy curve near $rv$. Using this, and replacing the first integral in Eq. (1) by 0.9999 $WDe$, gives \begin{equation}S=0.1010\ a\ W_{De}\end{equation} If a is not known, one can use the stretching force constant f for the X-Y bond. This is given by $f=d2U/dr2=2a2WDe$. Using the value of a obtained from this, Eq. (2) becomes \begin{equation}S=0.07142 (f\ W_{De})^{1/2},\end{equation} or \begin{equation}S=9.0419\ \mu\ dyn (f\ W_{De})^{1/2}\end{equation} when f is in microdynes per picometer and $WDe$ is in electron-volts. Previously, L. Pokras obtained for $f,WDe$, the values $51.211\mu$ dyn/pm, 5.2933 eV, for $HCl35$, and 51.194, 5.3211, for $HCl37$. Using these, $S(HCl35)=148.88$ and $S(HCl37)=149.24\mu dyn$. Values of S for other bonds, calculated from less reliable values of $WDe$ are: $CO385;N2370;C=C335;C=C221;NO263;O2221;OH167;H2138;NH133;CH132;C-C115;Cl282;Br262;I246;Li215;Na210;$ and $K26\mu dyn$. It is interesting to note that the S values of $C-C,C=C$, and $C=C$ are in the ratio 1 to 1.9 to 2.9.